Mitigation of transmission errors of quantized channel state information feedback in multi antenna systems

ABSTRACT

Methods are disclosed for improving communications on feedback transmission channels, in which there is a possibility of bit errors. The basic solutions to counter those errors are: proper design of the CSI vector quantizer indexing (i.e., the bit representation of centroid indices) in order to minimize impact of index errors, use of error detection techniques to expurgate the erroneous indices and use of other methods to recover correct indices.

TECHNICAL FIELD

Wireless communication using multiple antennas.

BACKGROUND

One of the most promising solutions for increased spectral efficiency inhigh capacity wireless systems is the use of multiple antennas on fadingchannels. The fundamental issue in such systems is the availability ofthe channel state information (CSI) at transmitters and receivers. Whileit is usually assumed that perfect CSI is available at the receivers,the transmitter may only have partial CSI available due to the feedbackdelay and noise, channel estimation errors and limited feedbackbandwidth, which forces CSI to be quantized at the receiver to minimizefeedback rate.

SUMMARY

Methods are disclosed for improving communications on feedbacktransmission channels, in which there is a possibility of bit errors.The basic solutions to counter those errors are: proper design of theCSI vector quantizer indexing (i.e., the bit representation of centroidindices) in order to minimize impact of index errors, use of errordetection techniques to expurgate the erroneous indices and use of othermethods to recover correct indices (see pending US patent application“Quantized channel state information prediction in multiple antennasystems” Ser. No. 11/852,206.) The content of U.S. Ser. No. 11/754,965and 11/852,206 are incorporated herein by reference.

There is provided a method of reducing the effect of errors in thefeedback of channel state information from a receiver to a transmitter.In an embodiment, the method comprises the steps of choosing multiplemappings of indices to channel states, estimating the effect ontransmission quality of feedback errors for each of the mappings ofindices to channel states, selecting a mapping of indices to channelstates to reduce the effect of feedback errors; and transmittingfeedback of channel state information from the receiver to thetransmitter, the receiver representing a channel state using thecodeword determined by the selected mapping of indices to channelstates.

These and other aspects of the method are set out in the claims, whichare incorporated here by reference.

BRIEF DESCRIPTION OF THE FIGURES

Embodiments will now be described with reference to the figures, inwhich like reference characters denote like elements, by way of example,and in which:

FIG. 1 is a schematic diagram showing the division of the channel statespace into Voronoi regions.

FIG. 2 shows the basic structure of the system proposed in U.S. patentapplication Ser. No. 11/754,965, and which may be used as modifiedaccording to the disclosed algorithms.

FIG. 3 a shows a good mapping of indices to centroids.

FIG. 3 b shows a bad mapping of indices to centroids.

FIG. 4 shows the general operation of an embodiment of an indexingoptimization algorithm.

FIG. 5 shows the operation of the initialization phase of the exemplaryindexing design algorithm of FIG. 4.

FIG. 6 shows the operation of the optimization phase of the exemplaryindexing design algorithm of FIG. 4.

FIG. 7 shows an embodiment of the system operation with error-detectingcodes.

FIG. 8 shows an embodiment of the system operation without errordetecting codes.

FIG. 9 shows a more general embodiment of an indexing algorithm.

DETAILED DESCRIPTION

In the typical CSI vector quantizer (VQ), the quantization of thechannel vector space is performed as in FIG. 1: the available space istessellated by Voronoi regions 20 with corresponding centroids 22 thatrepresent all vector realizations within each Voronoi region. The numberof such regions (centroids) is defined by the number of available bitsand each centroid is assigned an index 23 with the binary representationof length equal to the number of available feedback bits. The indicescan also be represented by arbitrary sequences of symbols, so long aseach index is represented by a unique sequence of symbols, and thesymbols can be transmitted by the feedback channel. When the receivertransmits its channel state information to the transmitter, it is thebits (or symbols) representing the centroid indices that are physicallysent over the feedback channel. When the term “binary index” is used,one could substitute “the sequence of symbols representing the index”.In the claims when a mapping of indices to channel states is mentioned,a mapping of symbol sequences to indices would serve the same purposeand so the claims should be construed to cover both.

All presented solutions can be used for both eigenmode and singularvalue codebooks in systems ranging from only one active receiver at atime to systems with multiple receivers being active simultaneously(where we define being active as receiving transmissions). The design ofthe feedback encoding solutions can be applied to quantized matrices oforthogonal eigenmodes, subsets of eigenmodes and scalar singular valuesas necessary. The following descriptions will be generic in form so thatthey can easily be applied to any type of CSI quantizing solution.

FIG. 2 shows the basic structure of the system proposed in U.S. patentapplication No. 11/754,965. The system works as follows:

-   -   1. Before the transmission epoch, each receiver 38 estimates 40        its channel matrix H for a feedforward channel 34 and uses this        information to perform the singular value decomposition (SVD) 42        of the matrix.    -   2. The eigenmode and singular value components are separately        quantized 44 using two codebooks V 46 and D 48, respectively.    -   3. The indices of the selected codewords are encoded 52, 54 and        fed back 56, 58 to the transmitter 36 on a feedback channel 50.    -   4. The transmitter includes an indexer and optimizer 66 which        uses all decoded 60, 62 indices 64 from all receivers in the        system to choose 68, 70 the preselected linear modulation and        power allocation matrices B and S, respectively. The choice is        based on a predefined set of rules (maximum fairness, throughput        etc.).    -   5. The input signal 72 is modulated using the modulation 74 and        power allocation 76 matrices, transmitted to the receiver over        the feedforward channel 34, using antennas 32, and the        transmitted modulated signal is processed 78 by the receiver.

The feedback channel 50 shown in FIG. 2 will inevitably suffer from thetransmission errors and the indices of the channel vectors reported bythe receivers will be erroneously decoded at the transmitter. Even ifthe feedback information is protected by channel codes, in a multipleuser scenario, it is possible that the interference will cause theindices to be detected with errors, which will lower the system'sthroughput.

For example, in FIG. 1, during the first part of the actual vectortrajectory 24, the centroid index number 3 represented by bits 011 wouldbe reported to the transmitter. However, if for some reason, the secondindex bit would be recovered with an error, the centroid index number 1(represented by bits 001) would instead be received by the transmitter,which would cause it to choose improper modulation matrices B and S (seeprevious section).

The basic transmission of the feedback indices 23 may comprise thefollowing steps:

-   -   1. Selection of the indices 23 representing the centroids 22        closest to the actual channel vectors.    -   2. (Optional) Adding error detection check bits to the binary        representation of the centroid indices.    -   3. (Optional) Adding channel error correction check bits.    -   4. Transmission of all the bits.    -   5. (Conditioned on 3) Performing channel decoding of the        received bits.    -   6. (Conditioned on 2) Performing error detection of the received        bits.    -   7. Reporting the received channel vector indices to the        optimizer/indexer in FIG. 2.    -   8. (Optional) Reporting which indices contain errors to the        optimizer/indexer in FIG. 2. This step can use results from 6 or        any alternative method as outlined later on.

Based on the above eight steps, the indexer will now be able to makedecision on the choice of modulation matrices for the next transmissionepoch. Three exemplary approaches to the problem are:

-   -   1. If error detection codes or any alternative error detection        method is used and the base station optimizer is aware of        erroneous receiver indices, it may discard them and only use the        correct ones in the optimization phase.    -   2. If error detection codes or any alternative error detection        method is used and the base station optimizer is aware of        erroneous receiver indices, it may attempt to recover them and        use all received indices (correct and recovered) in the        optimization phase.    -   3. If error detection is not used at all, the optimizer assumes        that the received indices are very close to the actual        transmitted indices and use them as if they were all correct.

A basic difference between methods 1, 2 and 3 lies in whether the errordetection methods are used to detect problems in channel informationindices fed back to the base station. If such methods are used, thetransmitter may recognize which indices are incorrect and can takeappropriate actions. If no error detection may be performed and thereceived indices are used ‘as-is’, the vector quantizer indexing must beproperly designed as shown in FIG. 3 a.

The mapping of the indices to the centroids in a quantizer is a complextask that can influence the system's performance tremendously whenerrors in the feedback link are not negligible. FIGS. 3 a and 3 b showsthe situation, where the identical vector quantizer has a differentmapping of indices 23 and the results of one bit error in thetransmission of the centroid indices.

In FIG. 3 a, the mapping was done in a way that ensured that one biterror in the last position of the index moved the centroid received atthe transmitter not far from the actual one. In other words, the smallHamming distance of the difference between the actual and receivedindices of the centroid corresponds to the small distance 26 between theactual centroids. The centroid distance 2-6 function will be discussedfurther in the document.

In FIG. 3 b, the small Hamming weight of index error does not correspondto the small centroid distance. In this case, a 1-bit error forces thecentroid to move far away from the actual one, which may have a verynegative influence on the system's performance.

The following algorithms are presented:

-   -   1. Design of the indexing for CSI MIMO vector quantizers.    -   2. Actual operation of the system using encoded feedback link        with CSI MIMO quantizers with or without error detection.

The algorithm for the design of the indexing can be carried out in anysuitable computing device, including for example pen and paper.Typically the design will be carried out prior to the initialization ofthe MIMO system.

The following notation will be used:

-   -   V_(k)—the kth centroid in codebook V.    -   k,l—indices of centroids in codebook V.    -   d_(kl)—the distance between the centroids specified by indices k        and l.    -   d(k;e)—distance profile for centroid V_(k) and a given number of        bit errors e.    -   GDP(e)—global distance profile for a given number of bit errors        e.    -   i,j—binary indices of a codeword in a vector quantizer.    -   H_(ij)—the Hamming distance between indices i and j.    -   I—the number of iterations of the index optimization algorithm    -   N—the length of the binary representation of centroid indices        i,j.

It is assumed that the indexing design follows the design of the channelvector quantizer V using any of the existing methods, for example themethod shown in the patent application “Quantization of channel stateinformation in multiple antenna systems” (U.S. patent Ser. No.11/754,965 pending). The input to the quantizer indexing algorithm isthe distance matrix D with number or rows and columns equal to thenumber of all centroids V_(k) (with our notation the number of rows andcolumns is equal to 2^(N)). The entries in the matrix are distancesbetween the centroids—for example, the kth row and lth entry is given byd_(kl). In particular, the entries on the diagonal of the matrix areequal to 0. The methods used to calculate the distance matrix D as wellas the centroid distances are immaterial in this patent application.However, some of the methods to calculate the centroid distances for thematrix D can be defined as follows:

-   -   1. d_(kl) is the angle between the centroids V_(k) and V_(l).    -   2. d_(kl) is the smaller of the angles between the centroids        V_(k) and V_(l) and between the centroids V_(k) and −V_(l).    -   3. d_(kl) is the Euclidean distance between the centroids V_(k)        and V_(l).    -   4. d_(kl) is the average system throughput loss when centroid        V_(k) is chosen instead of V_(l).    -   5. d_(kl) is the user system throughput loss when centroid V_(k)        is chosen instead of V_(l).    -   6. Any other distance definition depending on the system design        parameters

In addition to the distance metric d_(kl), representing a distancebetween two specified quantizer centroids, a set of distance profiles,d(k;e), and a global distance profile, GDP(e), are used to represent thedistance profile of the indexed quantizer. A distance profile d(k;e) fora given centroid k and a number of errors e represents a set of numberscorresponding to the distances between all erroneous representations ofthe centroid V_(k) and the actual centroid V_(k), assuming that e errorsappeared during the transmission of its corresponding index i. In otherwords,

d(k;e)=[d ₁ , d ₂ , d ₃ , . . . , d _(n) , . . . , d _(E)],

where E is the number of e-element subsets in N-long binaryrepresentation of codebook indices and d_(kl) corresponds to distancesd_(kl) between the centroid V_(k) and its erroneous version V_(l)containing e index errors.

Finally, to characterize the entire codebook, a global distance profileGDP(e) is defined as the union of all distance profiles d(k; e).Indexing design algorithm.

Design of the indexing based on the distance matrix D is performed usinga heuristic algorithm operating in two phases: the initialization phaseand optimization phase. Since the initialization phase of the algorithmdepends on random initial choice of indices, it is recommended that bothphases of the algorithm are repeated storing the index map after eachoptimization step for a given number of iterations I until the bestsolution has been found or the design constraint has been met. Thegeneral operation of the indexing design algorithm is shown in FIG. 4and described below.

General algorithm:

-   -   1. In step 80, initialize iteration counter i and in step 82 the        previous global distance profile GDP_(previous.)    -   2. In step 84, run the Initialization phase of the algorithm        (see below).    -   3. In step 86, run the Optimization phase of the algorithm (see        below).    -   4. In step 88, store index map and calculate the new global        distance profile GDP(e).    -   5. In step 90 compare GDP(e) with GDP_(previous); in step 92        check if GDP(e) improves GDP_(previous) and if so then in step        94 exchange GDP_(previous) with GDP(e) and store the current        index map.    -   6. In step 96 increase i by 1.    -   7. In step 98 if i <I go to 2.    -   8. In step 100, STOP.

Initialization phase:

-   -   1. In step 102, generate the distance matrix D; in step 104        initialize the lists of unassigned indices, centroids and        processed entries in D.    -   2. In step 106, find the smallest unprocessed entry d_(u)>0 in        the matrix D.    -   3. Mark the entry d_(kl) as processed.    -   4. In step 108 search for centroids V_(k) and V_(l)        corresponding to d_(kl); in step 110 check if any indices have        been assigned to either centroid. If neither centroids V_(k) nor        V_(l) corresponding to d_(kl) have been assigned any indices i        or j, in step 112 (a-c), step 118 (d-e) and step 120 (f):        -   a) Choose a random index i from the list of the unused            indices.        -   b) Assign the index i to the centroid V_(k).        -   c) Mark the ith entry in the list of used indices list as            taken.        -   d) Choose a random index j from the list of the unused            indices in such a way that the corresponding H_(ij) is            minimized.        -   e) Assign the index j to the centroid V_(l).        -   f) Mark the jth entry in the list of used indices list as            taken, and V_(l) as having an index assigned to it in the            list of used centroids.    -   5. In step 114, check if only one of the centroids V_(k) or        V_(l) have been assigned an index, and if so in step 118 (a-b)        and step 120 (c):        -   a) Choose a random index j from the list of the unused            indices in such a way that H_(ij) is minimum, where it is            assumed (step 116) that i is the binary index of the already            indexed centroid.        -   b) Assign the index j to the unassigned centroid.        -   c) Mark the jth entry in the list of used indices as taken,            and mark the unassigned centroid as assigned .    -   6. If both centroids V_(k) or V_(l) have been assigned an index,        go to 7.    -   7. In step 122, if there are still unassigned indices, go to 2.    -   8. In step 124, STOP.

The operation of the initialization phase is presented in FIG. 5.

After the completion of the initialization phase, all centroids V_(k) inthe codebook V have been assigned the binary indices i, with themajority of smallest distances d_(kl) in matrix D coupled to the binaryindices i and j with small Hamming distances. However, theinitialization phase can only reach locally optimum solutions and, inthe next step, an improved solution is iteratively searched for.

Optimization phase:

-   -   1. In step 130, generate the distance matrix D and initialize        the global distance profile GDP(e).    -   2. In step 132, initialize the list of processed entries in D.    -   3. In step 134, set the previous global error distance as        GDP_(previous)=GDP(e).    -   4. In step 136, find the smallest unprocessed entry d_(kl)>0 in        the matrix D, and mark it as processed.    -   5. In step 138, find the binary indices i and j assigned to the        centroids k and l. Choose whether to swap them as follows:        -   a) In step 140, calculate the global distance profile            GDP_(original)(e) with mapping of centroid V_(k) to binary            index i and centroid V_(l) to binary index j.        -   b) In step 142 and 144, calculate the global distance            profile GDP_(swapped)(e) with mapping of centroid V_(k) to            binary index j and centroid V_(l) to binary index i.        -   c) In step 146 choose the mapping corresponding to better            global distance profile from 6a) and 6b) and in step 148            assign the indices of centroids accordingly.    -   6. In step 150, check the list of the processed entries d_(kl),        and if there are still unprocessed entries, go to 4.    -   7. In step 152, calculate the GDP(e) with the current mapping of        centroids and indices. If it is better than GDP_(previous) then        go to 2.    -   8. In step 154, if there are no improvements over GDP_(previous)        STOP.

The operation of the optimization algorithm is presented in FIG. 6.

The optimization phase iteratively searches for better mapping betweencentroids and indices by swapping the binary representation of theclosest pairs. After each such swap, the global distance profile forswapped mapping is compared to the unswapped mapping and the globallybetter solution is chosen. The algorithm is repeated iteratively throughall centroids and stops when no improvement can be achieved byconsecutive swapping of the indices.

A more general version of this approach to indexing is shown in FIG. 9.In FIG. 5, pairs of centroids (that is, channel states representing aregion of channel state space for purposes of quantization) near oneanother in terms of the chosen distance measure are chosen and areassigned indices also near one another in Hamming distance, Hammingdistance being a proxy for the probability of one index being mistakenlyreceived as another (the less the distance, the more likely they will beconfused). Since the feedback bandwidth is limited, there will have tobe indices near one another in Hamming distance and the effect offeedback errors is reduced if such nearby indices are assigned to nearbychannel states, so as to reduce the effect on transmission quality ifthey are mistaken for one another. Hence the initialization phasedepicted in FIG. 5 can be regarded as choosing multiple mappings ofindices to channel states in step 220 (the different possibleassignments of indices to a pair of channel states), estimating theeffect of feedback errors of each in step 222 (using Hamming distance asa proxy in this case), and selecting one in step 224 (in this case onewith the minimum Hamming distance) so as to reduce the effect offeedback errors. Similarly the optimization phase shown in FIG. 6includes choosing multiple mappings of indices to channel states in step220 (in this case differing from one another by the swapping of pairs ofindices), estimating the effect of feedback errors of each mapping (inthis case using the global distance profile), and selecting a mapping toreduce the expected effect of feedback errors (by choosing the one withthe best global distance profile in this case). No matter how themapping is selected, it is used in step 226 to send feedback ofinformation concerning a channel state from a receiver to a transmitter,the receiver representing the channel state using the index mapped tothe exemplary state (eg. centroid) for the region of channel state spacein which the channel state lies.

System Operation with Error Detection in the Feedback Link

If the system uses error detecting codes in the feedback link, itsoperation can be summarized as follows:

-   -   1. In step 160, initialize transmission epoch to t=1.    -   2. In step 162, each receiver estimates its channel matrix H[t].    -   3. In step 164, each receiver performs the vector quantization        of the channel state information.    -   4. In step 166, the channel state information indices are        encoded using error detecting code (such as CRC).    -   5. (Optional) In step 168, the channel state information indices        with the error-detection redundancy are encoded using error        correcting code (such as convolutional or turbo codes).    -   6. In step 170, the encoded channel state information indices        are fed back to the transmitter.    -   7. (Conditional on 5) In step 172, the received channel state        information indices are decoded in a channel decoder that        attempts to correct possible channel transmission errors.    -   8. In step 174, the decoded indices are checked by an        error-detecting decoder.    -   9. In step 176, the receiver counts the number of erroneously        decoded indices.    -   10. Depending (in step 178) on the implementation, the receiver        may then:        -   a) In step 180, expurgate the erroneous indices, if there            are still enough indices for optimization process, and            process only the remaining ones        -   b) In step 184, ignore the errors and use the erroneous            indices.        -   c) In step 182, regenerate the erroneous indices, for            example, by using the channel prediction techniques from            pending US patent application “Quantized channel state            information prediction in multiple antenna systems” Ser. No.            11/852,206.    -   11. In step 186, the transmitter performs the selection of        active users using any method (maximum fairness, maximum        throughput etc.) and chooses the corresponding modulation        matrices.    -   12. The signal is transmitted to the selected active receivers.    -   13. In step 188, increase transmission epoch as t=t+1.    -   14. Go to 2.

The operation of the algorithm is presented in FIG. 7.

System Operation without Error Detection in the Feedback Link

If the system uses no error detecting codes in the feedback link, itsoperation can be summarized as follows:

-   -   1. In step 190, initialize transmission epoch to t=1.    -   2. In step 192, each receiver estimates its channel matrix H[t].    -   3. In step 194, each receiver performs the vector quantization        of the channel state information.    -   4. (Optional) In step 196, the channel state information indices        with the error-detection redundancy are encoded using error        correcting code (such as convolutional or turbo codes).    -   5. In step 198, the encoded channel state information indices        are fed back to the transmitter using the method described in        previous sections.    -   6. (Conditional on 4) In step 200, the received channel state        information indices are decoded in a channel decoder that        attempts to correct possible channel transmission errors.    -   7. If (step 202) the index error detection is possible using        alternative methods, for example, channel prediction techniques        such as the one presented in the pending US patent application        “Quantized channel state information prediction in multiple        antenna systems” Ser. No. 11/852,206, the transmitter may:        -   a. In step 206, expurgate the erroneous indices if there are            still enough indices for optimization process,        -   b. In step 204, regenerate the erroneous indices using, for            example, channel prediction techniques.    -   8. If (step 202) the index error detection is impossible, in        step 208 the receiver uses the received indices as correct ones,    -   9. In step 210, the transmitter performs the selection of active        users using any method (maximum fairness, maximum throughput        etc.) and chooses the corresponding modulation matrices.    -   10. The signal is transmitted to the selected active receivers.    -   11. In step 212, increase transmission epoch as t=t+1.    -   12. Go to 2.

The operation of the algorithm is presented in FIG. 8.

Immaterial modifications may be made to the embodiments described herewithout departing from what is covered by the claims. In the claims, theword “comprising” is used in its inclusive sense and does not excludeother elements being present. The indefinite article “a” before a claimfeature does not exclude more than one of the feature being present.Each one of the individual features described here may be used in one ormore embodiments and is not, by virtue only of being described here, tobe construed as essential to all embodiments as defined by the claims.

1-23. (canceled)
 24. A method of operating a multiple antenna communication system having a transmitter and a plurality of receivers, the method comprising: each receiver estimating its channel state; each receiver selecting a codebook index representing, according to an assignment of indices to channel states known to both the transmitter and the receiver, a predefined channel state near its respective estimated channel state; each receiver encoding its respective selected index using an error-detecting code; and each receiver transmitting its respective encoded index to the transmitter.
 25. The method of claim 24 wherein the channel state is characterized by a plurality of indices taken from multiple codebooks.
 26. The method of claim 24, further comprising: the transmitter decoding the encoded indices; the transmitter estimating the channel states based on the respective decoded indices; and the transmitter using the estimated channel state for data transmission to one or more of the receivers.
 27. The method of claim 26 wherein the channel codebook indices are encoded at the receivers using an error-correcting code, and decoded at the transmitter using an error-correcting decoder.
 28. The method of claim 26, the decoding comprising detecting erroneous indices and expurgating the erroneous indices in the decoded indices.
 29. The method of claim 26, the decoding comprising detecting erroneous indices and using the erroneous indices in the decoded indices.
 30. The method of claim 29 wherein the transmitter uses channel prediction in attempting to correct the erroneous indices.
 31. The method of claim 26, the decoding comprising detecting erroneous indices, attempting to correct erroneous indices, and including corrected indices in the decoded indices.
 32. A method of operating a multiple antenna communication system having a transmitter and multiple receivers, the method comprising: each receiver estimating its channel state; each receiver selecting a codebook index representing, according to an assignment of indices to channel states known to both the receiver and the transmitter, a predefined channel state near its respective estimated channel state; and each receiver transmitting its respective selected index to the transmitter.
 33. The method of claim 32 wherein the channel state is characterized by a plurality of indices taken from multiple codebooks
 34. The method of claim 32, further comprising: the transmitter transmitting information to one or more of the receivers, using the selected indices to estimate the channel state.
 35. The method of claim 34 wherein the channel codebook indices are encoded at the receivers using an error-correcting code, and decoded at the transmitter using an error-correcting decoder.
 36. The method of claim 34, further comprising the transmitter attempting to determine if each received channel codebook index is correct or erroneous.
 37. The method of claim 36 wherein the transmitter uses channel prediction to determine if each received channel codebook index is correct or erroneous.
 38. The method of claim 36 wherein the transmitter uses a form of prediction based on knowledge of an allowed subset of codebook indices out of all indices to determine if the received index is correct or erroneous.
 39. The method of claim 36 wherein the transmitter does not use channel codebook indices determined to be erroneous in transmitting to the receivers.
 40. The method of claim 39 wherein the transmitter uses channel prediction to recover channel codebook indices determined to be erroneous.
 41. The method of claim 36 wherein the transmitter uses channel codebook indices determined to be erroneous in transmitting to the receivers.
 42. The method of claim 36 wherein the transmitter attempts to recover channel codebook indices determined to be erroneous.
 43. A receiver for a multiple antenna communication system, the receiver comprising: a channel state estimation unit with access to a plurality of indices from multiple codebooks; and a codebook index selection unit connected to the channel state estimation unit with access to index assignment information for channel states known to both the receiver and at least one transmitter.
 44. A multiple antenna communication system comprising a plurality of receivers as defined in claim 43, and further comprising a transmitter disposed for transmitting information to at least one of the receivers by using indices selected by said receiver's codebook index selection unit to estimate the channel state. 